Semi-classical theory of nuclear shell structure

A stationary phase method for the Feynman's path-integral representation is explained and extended to the important case of an arbitrary spherical single-particle potential. Results are illustrated by examples of the infinite spherical potential well considered previously by Balian and Bloch, who used a different method and the deformed harmonic oscillator. Formal estimates are obtained for shell effects in the nuclear level density and in the nuclear binding energies (the shell energy corrections). Relationship to the numerical averaging is discussed. Factors essential for the appearance of pronounced shell structure in nuclei are considered. (author)